Surface flow formula (Water Overlay): Difference between revisions

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Imbalances in the water surface elevation across the grid drive the flow of water until a state of equilibrium is reached in terms of ''w'' (water surface elevation) and flux. Behavior of the flow is described by a second-order semi-discrete central-upwind scheme produced by Kurganov and Petrova (2007)<ref name="Kurganov2"/>, which is based on the 2-D Saint-Venant equations (a.k.a. shallow water equations):
Imbalances in water levels across the grid drive the flow of water until a state of equilibrium is reached in terms of ''h'' (the height of the water column) and flux. Behavior of the flow is described by a second-order semi-discrete central-upwind scheme produced by Kurganov and Petrova (2007)<ref name="Kurganov2"/>, which is based on the 2-D Saint-Venant equations (a.k.a. shallow water equations):


:<math>
:<math>
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\frac{\partial h}{\partial t} &+ \frac{\partial (hu)}{\partial x} + \frac{\partial (hv)}{\partial y} = 0,\\[3pt]
\frac{\partial h}{\partial t} &+ \frac{\partial (hu)}{\partial x} + \frac{\partial (hv)}{\partial y} = 0,\\[3pt]
\frac{\partial (hu)}{\partial t} &+ \frac{\partial}{\partial x} \left( hu^2 + \frac{1}{2} gh^2 \right) + \frac{\partial (huv)}{\partial y} = -gh \frac{\partial B}{\partial x} - ghn^2u \sqrt{u^2 + v^2} h^{-\frac{4}{3}},\\[3pt]
\frac{\partial (hu)}{\partial t} &+ \frac{\partial}{\partial x} \left( hu^2 + \frac{1}{2} gh^2 \right) + \frac{\partial (huv)}{\partial y} = -gh \frac{\partial B}{\partial x} - ghn^2u \sqrt{u^2 + v^2} h^{-\frac{4}{3}},\\[3pt]
\frac{\partial (hv)}{\partial t} &+ \frac{\partial (huv)}{\partial x} + \frac{\partial}{\partial y} \left( hv^2 + \frac{1}{2} gh^2 \right) = -gh \frac{\partial B}{\partial y} - ghn^2u \sqrt{u^2 + v^2} h^{-\frac{4}{3}},
\frac{\partial (hv)}{\partial t} &+ \frac{\partial (huv)}{\partial x} + \frac{\partial}{\partial y} \left( hv^2 + \frac{1}{2} gh^2 \right) = -gh \frac{\partial B}{\partial y} - ghn^2v \sqrt{u^2 + v^2} h^{-\frac{4}{3}},
\end{align}
\end{align}
</math>
</math>
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|}


==References==
{{article end
|seealso=
* [[Surface model (Water Overlay)|Surface model]]
* [[Result type (Water Overlay)|Water overlay result types]]
* [[Manning_value_(Function_Value)|Manning value]]
|references=
<references>
<references>
<ref name="Kurganov2">Kurganov A, Petrova G (2007) ∙ A Second-Order Well-Balanced Positivity Preserving Central-Upwind Scheme for the Saint-Venant System ∙ found at: http://www.math.tamu.edu/~gpetrova/KPSV.pdf (last visited 2019-04-11)</ref>
<ref name="Kurganov2">Kurganov A, Petrova G (2007) ∙ A Second-Order Well-Balanced Positivity Preserving Central-Upwind Scheme for the Saint-Venant System ∙ found at: http://www.math.tamu.edu/~gpetrova/KPSV.pdf (last visited 2019-04-11)</ref>
</references>
</references>
 
}}
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{{Template:WaterOverlay formula nav}}
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Latest revision as of 09:03, 29 January 2024

Imbalances in water levels across the grid drive the flow of water until a state of equilibrium is reached in terms of h (the height of the water column) and flux. Behavior of the flow is described by a second-order semi-discrete central-upwind scheme produced by Kurganov and Petrova (2007)[1], which is based on the 2-D Saint-Venant equations (a.k.a. shallow water equations):

where

u is the velocity in the x-direction
v is the velocity in the y-direction
h is the water depth
B is the bottom elevation
g is the acceleration due to gravity
n is the Gauckler–Manning coefficient

See also

References

  1. ↑ Kurganov A, Petrova G (2007) ∙ A Second-Order Well-Balanced Positivity Preserving Central-Upwind Scheme for the Saint-Venant System ∙ found at: http://www.math.tamu.edu/~gpetrova/KPSV.pdf (last visited 2019-04-11)
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